<<

. 2
( 2)






WHAT PROJECTS WILL BE ACCEPTED, BY EITHER NPV OR IRR? PROJECTS A, B, C, AND D.
IF THE SAME SITUATION EXISTS YEAR AFTER YEAR, AT WHAT RATE OF RETURN WILL CASH FLOWS FROM EARLIER YEARS' INVESTMENTS BE REINVESTED? CAPITAL BUDGETING DECISIONS ARE MADE IN THIS SEQUENCE: (1) THE COMPANY WOULD SAY, "WE CAN TAKE ON A, B, C, AND D AND FINANCE THEM WITH 10% MONEY, SO LET'S DO IT." (2) THEN IT WOULD GET CASH FLOWS FROM EARLIER YEARS' PROJECTS. WHAT WOULD IT DO WITH THOSE CASH FLOWS? IT WOULD USE THEM IN LIEU OF RAISING MONEY THAT COSTS 10%, SO IT WOULD SAVE 10%. THEREFORE, 10% IS THE OPPORTUNITY COST OF THE CASH FLOWS. IN EFFECT, CASH FLOWS ARE REINVESTED AT THE 10% COST OF CAPITAL.
NOTE, HOWEVER, THAT NPV AND IRR ALWAYS GIVE THE SAME ACCEPT/REJECT DECISIONS FOR INDEPENDENT PROJECTS, SO IRR CAN BE USED JUST AS WELL AS NPV WHEN INDEPENDENT PROJECTS ARE BEING EVALUATED. THE NPV VERSUS IRR CONFLICT ARISES ONLY IF MUTUALLY EXCLUSIVE PROJECTS ARE INVOLVED.


H. 1. DEFINE THE TERM MODIFIED IRR (MIRR). FIND THE MIRRs FOR PROJECTS L
AND S.

ANSWER: MIRR IS THAT DISCOUNT RATE WHICH EQUATES THE PRESENT VALUE OF THE TERMINAL VALUE OF THE INFLOWS, COMPOUNDED AT THE COST OF CAPITAL, TO THE PRESENT VALUE OF THE COSTS. HERE IS THE SETUP FOR CALCULATING PROJECT L'S MODIFIED IRR:

0 1 2 3
| | | |
PV OF COSTS = (100.00) 10 60 80.00
66.00
12.10
TV OF INFLOWS = 158.10

PV OF TV = 100.00
= $100 = .

PV COSTS = = = .

AFTER YOU CALCULATE THE TV, ENTER N = 3, PV = -100, PMT = 0, FV = 158.1, AND THEN PRESS I TO GET THE ANSWER, MIRRL = 16.5%. WE COULD CALCULATE MIRRS SIMILARLY: = 16.9%. THUS, PROJECT S IS RANKED HIGHER THAN L. THIS RESULT IS CONSISTENT WITH THE NPV DECISION.


H. 2. WHAT ARE THE MIRR'S ADVANTAGES AND DISADVANTAGES VIS-A-VIS THE REGULAR IRR? WHAT ARE THE MIRR'S ADVANTAGES AND DISADVANTAGES VIS-A-VIS THE NPV?

ANSWER: MIRR IS A BETTER RATE OF RETURN MEASURE THAN IRR FOR TWO REASONS: (1) IT CORRECTLY ASSUMES REINVESTMENT AT THE PROJECT'S COST OF CAPITAL RATHER THAN AT ITS IRR. (2) MIRR AVOIDS THE PROBLEM OF MULTIPLE IRRs--THERE CAN BE ONLY ONE MIRR FOR A GIVEN PROJECT.
MIRR DOES NOT ALWAYS LEAD TO THE SAME DECISION AS NPV WHEN MUTUALLY EXCLUSIVE PROJECTS ARE BEING CONSIDERED. IN PARTICULAR, SMALL PROJECTS OFTEN HAVE A HIGHER MIRR, BUT A LOWER NPV, THAN LARGER PROJECTS. THUS, MIRR IS NOT A PERFECT SUBSTITUTE FOR NPV, AND NPV REMAINS THE SINGLE BEST DECISION RULE. HOWEVER, MIRR IS SUPERIOR TO THE REGULAR IRR, AND IF A RATE OF RETURN MEASURE IS NEEDED, MIRR SHOULD BE USED.
BUSINESS EXECUTIVES AGREE. AS NOTED IN THE TEXT, BUSINESS EXECUTIVES PREFER TO COMPARE PROJECTS' RATES OF RETURN TO COMPARING THEIR NPVs. THIS IS AN EMPIRICAL FACT. AS A RESULT, FINANCIAL MANAGERS ARE SUBSTITUTING MIRR FOR IRR IN THEIR DISCUSSIONS WITH OTHER CORPORATE EXECUTIVES. THIS FACT WAS BROUGHT OUT IN THE OCTOBER 1989 FMA MEETINGS, WHERE EXECUTIVES FROM DU PONT, HERSHEY, AND AMERITECH, AMONG OTHERS, ALL REPORTED A SWITCH FROM IRR TO MIRR.


I. AS A SEPARATE PROJECT (PROJECT P), THE FIRM IS CONSIDERING SPONSORING A PAVILION AT THE UPCOMING WORLD'S FAIR. THE PAVILION WOULD COST $800,000, AND IT IS EXPECTED TO RESULT IN $5 MILLION OF INCREMENTAL CASH INFLOWS DURING ITS 1 YEAR OF OPERATION. HOWEVER, IT WOULD THEN TAKE ANOTHER YEAR, AND $5 MILLION OF COSTS, TO DEMOLISH THE SITE AND RETURN IT TO ITS ORIGINAL CONDITION. THUS, PROJECT P'S EXPECTED NET CASH FLOWS LOOK LIKE THIS (IN MILLIONS OF DOLLARS):

YEAR NET CASH FLOWS
0 ($0.8)
1 5.0
2 (5.0)

THE PROJECT IS ESTIMATED TO BE OF AVERAGE RISK, SO ITS COST OF CAPITAL IS 10 PERCENT.

I. 1. WHAT IS PROJECT P’S NPV? WHAT IS ITS IRR? ITS MIRR?

ANSWER: HERE IS THE TIME LINE FOR THE CASH FLOWS, AND THE NPV:

0 1 2
| | |
-800,000 5,000,000 -5,000,000

NPVP = -$386,776.86.

WE CAN FIND THE NPV BY ENTERING THE CASH FLOWS INTO THE CASH FLOW REGISTER, ENTERING I = 10, AND THEN PRESSING THE NPV BUTTON. HOWEVER, CALCULATING THE IRR PRESENTS A PROBLEM. WITH THE CASH FLOWS IN THE REGISTER, PRESS THE IRR BUTTON. AN HP-10B FINANCIAL CALCULATOR WILL GIVE THE MESSAGE "ERROR-SOLN." THIS MEANS THAT PROJECT P HAS MULTIPLE IRRs. AN HP-17B WILL ASK FOR A GUESS. IF YOU GUESS 10%, THE CALCULATOR WILL PRODUCE IRR = 25%. IF YOU GUESS A HIGH NUMBER, SUCH AS 200%, IT WILL PRODUCE THE SECOND IRR, 400%. THE MIRR OF PROJECT P = 5.6%, AND IS FOUND BY COMPUTING THE DISCOUNT RATE THAT EQUATES THE TERMINAL VALUE ($5.5 MILLION) TO THE PRESENT VALUE OF COST ($4.93 MILLION).


I. 2. DRAW PROJECT P'S NPV PROFILE. DOES PROJECT P HAVE NORMAL OR NON-NORMAL CASH FLOWS? SHOULD THIS PROJECT BE ACCEPTED?

ANSWER: YOU COULD PUT THE CASH FLOWS IN YOUR CALCULATOR AND THEN ENTER A SERIES OF I VALUES, GET AN NPV FOR EACH, AND THEN PLOT THE POINTS TO CONSTRUCT THE NPV PROFILE. WE USED A SPREADSHEET PROGRAM TO AUTOMATE THE PROCESS AND THEN TO DRAW THE PROFILE. NOTE THAT THE PROFILE CROSSES THE X-AXIS TWICE, AT 25% AND AT 400%, SIGNIFYING TWO IRRs. WHICH IRR IS CORRECT? IN ONE SENSE, THEY BOTH ARE--BOTH CAUSE THE PROJECT'S NPV TO EQUAL ZERO. HOWEVER, IN ANOTHER SENSE, BOTH ARE WRONG--NEITHER HAS ANY ECONOMIC OR FINANCIAL SIGNIFICANCE.
PROJECT P HAS NONNORMAL CASH FLOWS; THAT IS, IT HAS MORE THAN ONE CHANGE OF SIGNS IN THE CASH FLOWS. WITHOUT THIS NONNORMAL CASH FLOW PATTERN, WE WOULD NOT HAVE THE MULTIPLE IRRs.
SINCE PROJECT P'S NPV IS NEGATIVE, THE PROJECT SHOULD BE REJECTED, EVEN THOUGH BOTH IRRs (25% AND 400%) ARE GREATER THAN THE PROJECT'S 10 PERCENT COST OF CAPITAL. THE MIRR OF 5.6% ALSO SUPPORTS THE DECISION THAT THE PROJECT SHOULD BE REJECTED.



J. IN AN UNRELATED ANALYSIS, AXIS MUST CHOOSE BETWEEN THE FOLLOWING TWO MUTUALLY EXCLUSIVE PROJECTS:

EXPECTED NET CASH FLOWS
YEAR PROJECT S PROJECT L
0 ($100,000) ($100,000)
1 60,000 33,500
2 60,000 33,500
3 -- 33,500
4 -- 33,500

THE PROJECTS PROVIDE A NECESSARY SERVICE, SO WHICHEVER ONE IS SELECTED IS EXPECTED TO BE REPEATED INTO THE FORESEEABLE FUTURE. BOTH PROJECTS HAVE A 10 PERCENT COST OF CAPITAL.

J. 1. WHAT IS EACH PROJECT'S INITIAL NPV WITHOUT REPLICATION?

ANSWER: THE NPVs, FOUND WITH A FINANCIAL CALCULATOR, ARE CALCULATED AS FOLLOWS:

INPUT THE FOLLOWING: CF0 = -100000, CF1 = 60000, NJ = 2, AND I = 10 TO SOLVE FOR NPVS = $4,132.23 ? $4,132.

INPUT THE FOLLOWING: CF0 = -100000, CF1 = 33500, NJ = 4, AND I = 10 TO SOLVE FOR NPVL = $6,190.49 ? $6,190.

HOWEVER, IF WE MAKE OUR DECISION BASED ON THE RAW NPVs, WE WOULD BE BIASING THE DECISION AGAINST THE SHORTER PROJECT. SINCE THE PROJECTS ARE EXPECTED TO BE REPLICATED, IF WE INITIALLY CHOOSE PROJECT S, IT WOULD BE REPEATED AFTER 2 YEARS. HOWEVER, THE RAW NPVs DO NOT REFLECT THE REPLICATION CASH FLOWS.


J. 2. NOW APPLY THE REPLACEMENT CHAIN APPROACH TO DETERMINE THE PROJECTS’ EXTENDED NPVs. WHICH PROJECT SHOULD BE CHOSEN?

ANSWER: THE SIMPLE REPLACEMENT CHAIN APPROACH ASSUMES THAT THE PROJECTS WILL BE REPLICATED OUT TO A COMMON LIFE. SINCE PROJECT S HAS A 2-YEAR LIFE AND L HAS A 4-YEAR LIFE, THE SHORTEST COMMON LIFE IS 4 YEARS. PROJECT L'S COMMON LIFE NPV IS ITS RAW NPV:

COMMON LIFE NPVL = $6,190.

HOWEVER, PROJECT S WOULD BE REPLICATED IN YEAR 2, AND IF WE ASSUME THAT THE REPLICATED PROJECT'S CASH FLOWS ARE IDENTICAL TO THE FIRST SET OF CASH FLOWS, THEN THE REPLICATED NPV IS ALSO $4,132, BUT IT "COMES IN" IN YEAR 2. WE CAN PUT PROJECT S'S CASH FLOW SITUATION ON A TIME LINE:

0 1 2 3 4
| | | | |
4,132 4,312
3,415
7,547

HERE WE SEE THAT S'S COMMON LIFE NPV IS NPVS = $7,547.
THUS, WHEN COMPARED OVER A 4-YEAR COMMON LIFE, PROJECT S HAS THE HIGHER NPV, HENCE IT SHOULD BE CHOSEN. PROJECT S WOULD HAVE THE HIGHER NPV OVER ANY COMMON LIFE.


J. 3. NOW ASSUME THAT THE COST TO REPLICATE PROJECT S IN 2 YEARS WILL INCREASE TO $105,000 BECAUSE OF INFLATIONARY PRESSURES. HOW SHOULD THE ANALYSIS BE HANDLED NOW, AND WHICH PROJECT SHOULD BE CHOSEN?

ANSWER: IF THE COST OF PROJECT S IS EXPECTED TO INCREASE, THE REPLICATION PROJECT IS NOT IDENTICAL TO THE ORIGINAL, AND THE EAA APPROACH CANNOT BE USED. IN THIS SITUATION, WE WOULD PUT THE CASH FLOWS ON A TIME LINE AS FOLLOWS:

0 1 2 3 4
| | | | |
-100,000 60,000 60,000 60,000 60,000
-105,000
- 45,000

COMMON LIFE NPVS = $3,415.

WITH THIS CHANGE, THE COMMON LIFE NPV OF PROJECT S IS LESS THAN THAT FOR PROJECT L, AND HENCE PROJECT L SHOULD BE CHOSEN.


K. AXIS IS ALSO CONSIDERING ANOTHER PROJECT WHICH HAS A PHYSICAL LIFE OF 3 YEARS; THAT IS, THE MACHINERY WILL BE TOTALLY WORN OUT AFTER 3 YEARS. HOWEVER, IF THE PROJECT WERE TERMINATED PRIOR TO THE END OF 3 YEARS, THE MACHINERY WOULD HAVE A POSITIVE SALVAGE VALUE. HERE ARE THE PROJECT’S ESTIMATED CASH FLOWS:

INITIAL INVESTMENT END-OF-YEAR
AND OPERATING NET SALVAGE
YEAR CASH FLOWS VALUE_
0 ($5,000) $5,000
1 2,100 3,100
2 2,000 2,000
3 1,750 0

USING THE 10 PERCENT COST OF CAPITAL, WHAT IS THE PROJECT’S NPV IF IT IS OPERATED FOR THE FULL 3 YEARS? WOULD THE NPV CHANGE IF THE COMPANY PLANNED TO TERMINATE THE PROJECT AT THE END OF YEAR 2? AT THE END OF YEAR 1? WHAT IS THE PROJECT’S OPTIMAL (ECONOMIC) LIFE?

ANSWER: HERE ARE THE TIME LINES FOR THE 3 ALTERNATIVE LIVES:


NO TERMINATION:

0 1 2 3
| | | |
-5,000 2,100 2,000 1,750
0
1,750

NPV = -$123.

TERMINATE AFTER 2 YEARS:

0 1 2
| | |
-5,000 2,100 2,000
2,000
4,000

NPV = $215.

TERMINATE AFTER 1 YEAR:

0 1
| |
-5,000 2,100
3,100
5,200

NPV = -$273.

WE SEE (1) THAT THE PROJECT IS ACCEPTABLE ONLY IF OPERATED FOR 2 YEARS,AND (2) THAT A PROJECT'S ENGINEERING LIFE DOES NOT ALWAYS EQUAL ITS ECONOMIC LIFE.

<<

. 2
( 2)